The excess of pressure in a first soap bubble is three times that of other soap bubble. Then the ratio of the volume of first bubble to other is
The radii of two soap bubbles are $$r_1$$ and $$r_2$$. In isothermal condition they combine with each other to form a single bubble. The radius of resultant bubble is
The work done in blowing a soap bubble of radius $$\mathrm{R}$$ is '$$\mathrm{W}_1$$' at room temperature. Now the soap solution is heated. From the heated solution another soap bubble of radius $$2 \mathrm{R}$$ is blown and the work done is '$$\mathrm{W}_2$$'. Then
A steel coin of thickness '$$\mathrm{d}$$' and density '$$\rho$$' is floating on water of surface tension '$$T$$'. The radius of the coin $$(R)$$ is [$$\mathrm{g}=$$ acceleration due to gravity]